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A Textbook of Matrix Algebra by Jayesh M. Dhodiya

A Textbook of Matrix Algebra

by Jayesh M. Dhodiya
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Book cover type: Paperback
  • ISBN13: 9781922617385
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Central West Publishing
  • Publisher Imprint: Central West Publishing
  • Publication Date:
  • Pages: 480
  • Original Price: USD 124.99
  • Language: English
  • Edition: N/A
  • Item Weight: 640 grams
  • BISAC Subject(s): Teaching / Subjects / Mathematics and Algebra / General

In order to provide a balanced and comprehensive account of matrix algebra, this book covers the core theory and methods in matrix analysis. The book consists of eight chapters. Chapter 1 is an introduction to matrices that introduces matrices using real-world examples, basic definitions and operations of matrix algebra. This chapter also includes solutions of the algebraic system of equations by matrix theory. Chapter 2 introduces the rank theory and its applications. This chapter includes the solution of simultaneous non-Homogeneous and homogeneous equations and methods to identify linear dependence and linear independence of vectors. Chapter 3 introduces eigenvalues and eigenvectors with their properties and importance. This chapter also includes Cayley Hamilton Theorem and its applications. Chapter 4 discusses special operations on matrices. The chapter also includes diagonalization-powers of a square matrix, orthogonalization of a symmetric matrix and Sylvester Theorem. Chapter 5 deals with the quadratic forms of matrices. This chapter presents canonical form, Lagrange's method of reduction of a quadratic form to the diagonal form and reduction to canonical form by orthogonal transformation. Chapter 6 introduces different kinds of real and complex matrices and their properties. Chapter 7 and chapter 8 introduce different methods to solve the linear system of equations and their limitations. Chapter 7 discusses Cramer's rule (methods of determinant), method of matrix inversion, Gauss elimination Method, Gauss Jordan Method, Cholesky's triangularization method, triangularization of a symmetric matrix, LU decomposition method/Crout's method, whereas chapter 8 deals with the numerical solution of the linear system of equations. These chapters include the iterative method (Jacobi method), the Gauss- Seidel method and successive over relaxation method (SOR).


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